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676                      Curves of Crank Effort.

obtained.    The revolving parts must be balanced by opposing
weights on the crank shaft.

Curves of Crank Effort.—If the crank be on either dead
centre, there is no tangential or turning effect produced by the
steam pressure on the piston, all such pressure being received
upon the bearings. When the crank is midway between dead
points the whole piston pressure is transmitted tangentially, and
there is no pressure on the bearings except that due to dead
weight. Between the two conditions part of the pressure is
transmitted tangentially and part normally. But (p. 491) the
polar curve proportionally represents tangential crank pressures,
other things being equal. Divide then jo, Fig. 660, into tenths
and measure the radii vector of the curve UK in terms of these
divisions: the numbers obtained will represent the virtual crank
arms in relation to pressures transmitted along ABO. Taking the
total pressures from A to B, multiply each pressure ordinate by its
virtual crank arm, and the result will be the tangential crank
pressure for that position. Setting out these results radially, with
the crank circle JKLM as a base line, we obtain the two curves of
crank effort ighji. and L-klm] for the top and bottom of piston
respectively. These again are better understood on a straight
base, so the base JK is stepped out at co, KL at OD, and the
radial ordinates transferred as vertical ordinates on the new base
CD. Curves CHD and D/C are thus arrived at.

Combination of Crank Effort Diagrams.—Though
the fly wheel may equalise very tolerably the crank effort, there is
still the difficulty of starting when the crank is at either dead
centre. This is not a material difficulty for a factory engine
which has only to be started twice a day; but in locomotive and
marine practice it would be a very serious obstacle. In loco-
motives two cranks at right angles are employed, as at i a, Fig.
447, p. 486, while in marine practice it is usual to place three
cranks at 120° mutually. The latter gives the best conditions, but
the advantage of both will be made clear in Fig. 661.

At (a) two cranks set at 90° are each supposed to have effort
curves, as in Fig, 660. Plot these with relation to the respective
cranks, A A being the top curves, and BB the bottom ones. Then
the curve of total effort may be found by super-position, that is, at